In a subband implementation of an echo canceler, or more generally, any adaptive filter, the signals to be processed, i.e., a receive signal and a transmit signal, are first decomposed into an array of frequency bands and, then, processing is done on a per-band basis. To this end, an X-analysis filter bank is employed to decompose the receive signal x(k) into a predetermined number of frequency bands and a Y-analysis filter bank is employed to decompose the transmit signal y(k) into a similar number of frequency bands. Then, the The X and Y subband signals are supplied to an echo canceler in each respective subband in order to cancel echos in the respective subbands. One such subband echo canceler is disclosed in U.S. Pat. No. 5,272,695 issued Dec. 21, 1993.
In prior subband echo cancelers, the X and Y filters in the X and Y analysis filter banks and were identical. That is, they had identical frequency characteristics and, consequently, there was overlap in the roll-off regions of the frequency characteristics. It has been observed that the prior subband echos cancelers using such filters in the X and Y analysis filter banks with identical frequency characteristics for the subbands suffer in convergence performance. Indeed, poor convergence at band edges, that is, at frequencies covered roughly equally by two adjacent subbands has been observed. An explanation for the poor band-edge convergence is that the correlation matrices of subsampled per-band reference signals (that is, the X subband signals running down the tap delay lines of the echo cancelers in each subband) are ill conditioned with small eigenvalues. If eigenmodes associated with these small eigenvalues are excited, there will inevitably be long time constants introduced into the convergence of the echo cancelers in the subbands. The result is that there is practically no convergence of the subband echo cancelers in the transition regions between subbands. This is extremely undesirable.